Bunuel
Is the length of rectangular field F greater than the length of rectangular field G ?
(1) The area of F is greater than the area of G.
(2) The width of F is less than the width of G.
DS96502.01
Quantitative Review 2020 NEW QUESTION
In this case, individually, we are able to fairly quickly discern that just the area of F being greater (statement
(1)) - or just the width of F being less (statement
(2)) cannot be enough information, as we can both answer the question "yes" and "no" within those parameters. So, we'll want to think about whether both statements together are sufficient or neither is sufficient.
When we take the statements together, in order to have a larger area, the (length)*(width) will need to be larger.
So, if we know we have a smaller width - we can conceptually conclude that the length of rectangular field F will need to be greater than the length of rectangular field G
(smaller length)*
(larger width) must be true in order to be > (larger length)*(smaller width)
Basically, the length must be larger to outweigh the smaller width and create a greater outcome for (length)*(width).
So, since the length of F
must be greater in order for the statements combined to hold true - together, the statements are sufficient!
(C)Since the overlap of the two statements creates a situation such that the length
must be larger, we are able to conclude sufficiency. David makes a great point above in that this would not be the case if we were told that the width of F was greater, this would not be enough information - even together - as we could still answer the question "yes" and answer it "no."
It is specifically because we have the must be true parameter around the length being greater that we are able to conclude sufficiency. We know the answer must be "yes."
Hope this helps!